This study presents a 2-SIP model for inventory replenishment and the administration of
childhood vaccines in targeted immunization outreach sessions. To the best of our knowledge, this
is the first stochastic optimization model which captures the relationships that exist among these
decisions . The model presented here minimizes replenishment and OVW costs. OVW represent the
doses not used by the end of an immunization session. Unlike related works in the literature and the
current practice that relies on the use of a single multi-dose vial, this study models the performance
of an inventory replenishment policy that allows a mix of multi-dose vials for vaccination. An
extensive numerical analysis is conducted to evaluate the performance of the proposed policy and
to compare to other simple-to-implement vaccine administration policies.
In order to solve the proposed 2-SIP, the LS method is extended by incorporating GMI and
MRI cuts in the first-stage problem. Via an extensive numerical study we show that the proposed
algorithm is scalable; it outperforms the LS method by providing high quality solutions in a much
shorter CPU time.
After developing a case study using real-world data from Bangladesh, a sensitivity analysis
is conducted to evaluate the system’s behavior. Our observations can be summarized as follows:
1. Population size impacts decisions about the mix of multi-dose vials to use in a region. The
use of multi-dose with complementary single-dose vials is recommended in highly populated
regions.
2. Vaccine purchasing costs impact the achievable immunization levels within a given budget limit.
Thus, the models presented here aid policy makers in negotiating the necessary subsidies to
achieve the targeted vaccination coverage levels.
lengths that are the same length as the vaccine’s safe use time do minimize the total cost.
Short sessions in sparsely populated regions also minimize costs and OVW.
These observations motivated the design of vaccine administration policies that are simple
and economical. Numerical results demonstrate that the WO policy has the lowest total costs and
therefore, is highly recommended. For highly populated and well-connected regions, FMLS policy
works well since it provides high vaccine coverage level at a lower cost. Moreover, in regions that
can only use single multi-dose vials, the decision about the size of a vial to use should be based on
population size, birth rate, and the number of clinics in the region (see Table (2.5)).
We plan to extend this research in the following ways. First, since no clear guidelines
determine the number of scenarios used, investigating applications of sequential sampling algorithms,
such as the two-stage stochastic decomposition (SD) method [62], is necessary. The SD method was
originally designed for 2-SLPs and does not require a priori selection of scenarios. Since the model
presented here is an MILP, we plan to extend this method to accommodate discrete decision variables
in the first stage. Second, this proposed model identifies inventory replenishment decisions of a single
outreach session, so we plan to extend this model to consider multiple sessions organized by the same
clinic, as well as multiple clinics within a region. We expect that these clinics will coordinate their
own decisions about inventory and operating hours to minimize costs and OVW. Third, we plan to
develop an extension of the proposed model to aid replenishment decisions in clinics that handle
different types of vaccines with different safe use times, such as liquid with 28 days and lyophilized
1.5 2 2.5 3 3.5 4 4.5 5 5.5 Total Cost ($) 104 0 0.2 0.4 0.6 0.8 1 Estimated cdf FMLS Policy Base policy SDSL policy WO policy 1-dose 2-dose 10-dose 2.22 2.225 104 0.798 0.8 0.802 0.804 0.806 0.808
(a) Total cost.
0 50 100 150 200
Number of unserved patients 0.4 0.5 0.6 0.7 0.8 0.9 1 Estimated cdf FMLS Policy Base policy SDS policy WO policy 1-dose 2-dose 10-dose 6 8 10 12 0.72 0.73 0.74 0.75 (b) Unserved patients. 0 100 200 300 400 500 600
Number of doses wasted 0 0.2 0.4 0.6 0.8 1 Estimated cdf FMLS Policy Base policy SDS policy WO policy 2-dose 10-dose 275 280 285 290 295 0.09 0.1 0.11 0.12 0.13 (c) OVW.
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
Incentive cost per patient ($)
10 20 30 40 50 60 70 80 90 100 Moved patients (%)
(a) Incentive cost versus the percent of people who
attend. (b) The hourly consumption schedule and waited peo-ple.
Chapter 3
A Two-Stage Stochastic Model for
Joint Pricing Inventory
Replenishment with Deteriorating
Products
3.1
Introduction
This work focuses on the analysis of joint pricing and inventory management decisions
for age-dependent perishable products in a periodic-review inventory system. An age-dependent
perishable product loses its quality/value and quantity the longer it stays in the shelves, and it is
disposed after a certain time. Examples of such products are fruits, and vegetables in grocery stores;
or baked goods in bakeries. Since demand for perishable products is price sensitive, businesses offer
price markdowns to stimulate demand for products which are approaching the end of their shelf
life. The same product type, at different stage of shelf life and price, coexist in the market. Thus,
different from the case when the inventory does not perish, models for joint pricing and inventory
management of perishable products take into account the age of inventories. The proposed model
waste and disposal cost for perished products.
The motivation for this research are the opportunities we see to reduce waste of perishable
products by integrating inventory management policies with pricing and markdown decisions; and
to manage the profitability of perishables in retailing using pricing. For example, ERS of USDA
estimated that, in 2010, 45 billion pounds of available food at retail stores in the United States was
wasted [25]. Moreover, about 40% of the annual agricultural production was wasted while 17% of
the population was undernourished in 2014 in India [21]. In addition to social impacts, wastage has
negative environmental impacts. For example, in the United States food waste accounts for 10% of
the energy supplied, 80% of consumed water, and 50% of land used [56].
A number of studies in the literature propose control policies to optimize the performance
of inventory management systems. Early works in this area assumed that the product has a single
static price which is exogenous to the inventory management problem [48]. In these works, inventory
management and pricing decisions were made in isolation for two main reasons. First, the data
available was insufficient to characterize the impact that price and markdowns have on demand.
Second, the benefits from improved inventory management were perceived as additive to the benefits
from pricing. In recent works, we have seen an increased interest on integrating pricing and inventory
management decisions in retail and other industries [49]. This is due to the increased availability
of data and the development of decision support tools for analyzing the impacts of pricing and
markdowns on inventory management decisions. Technologies available today (such as, point-of-sale
data and loyalty programs) provide companies with ample data about customers’ purchasing history
and preferences which can be used to estimate the impact of price on customer demand. Indeed,
inventory replenishment strategies control the supply side of a business whereas pricing policies
control the demand side. Integrating these decisions mitigates the risk of mismatch in supply and
demand, and increases profitability [128].
It has been noted in the literature [130, 124] that customers are willing to pay less for
perishable products which are approaching their expiration date since they may perceive these
products as of lower quality. Many industries nowadays are dealing with shorter product life-
cycles. Thus, even when a product’s quality is not impacted (such as smart phones), the willingness
of customers to pay the full price decreases when a new version of the product appears in the
market. Businesses use price markdowns to reduce losses from wastage of perishable products.
retailers markdown vegetables, fruits, dairy, and bakery goods by as much as 40% to 50%.
Replenishment decisions for perishable products are challenging due to uncertainties of
customer demand which are caused by limited product shelf life and price markdowns. These
decisions are further complicated by uncertainties in the amount and quality of shipments received
from suppliers. Dual-sourcing is a policy often used by retailers to mitigate the risks of supply and
demand uncertainties [84].
This study proposes a stochastic optimization model that integrates inventory replenishment
and pricing decisions for age-dependent perishable products in a periodic-review inventory system.
We express the stochastic demands for new and old products as linear functions of their prices.
The model determines suppliers and corresponding replenishment quantities which balance product
waste (as a result of too much inventory) and product shortage (as a result of too little inventory).
We consider a single markdown which is typically the case in grocery stores. This perishable product
is produced by two suppliers. One of the suppliers is reliable but expensive. The other supplier, is
not reliable since it has limited and varying capacity. However, this supplier is less expensive. The
proposed model captures the trade-offs that exits between timing of markdown and waste, size of
markdown and waste, size of markdown and profits, and supply chain costs and reliability.
The proposed model captures many interrelated and conflicting relationships. We develop
a case study and conduct an extensive sensitivity analysis to demonstrate the nature of these rela-
tionships. This analysis reveals trends which are neither intuitive, nor easy to estimate. We expect
that our results will provide insightful perspectives to managers making inventory replenishment
decisions for perishable products.